Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample230.0ms

Algorithm

intervals

Results

71.0ms	126×	body	1280	valid
39.0ms	33×	body	1280	nan
27.0ms	52×	body	640	valid
27.0ms	34×	body	640	nan
13.0ms	74×	body	80	overflowed
11.0ms	14×	body	640	invalid
7.0ms	24×	body	320	valid
5.0ms	12×	body	320	nan
5.0ms	4×	body	1280	invalid
4.0ms	40×	body	80	valid
3.0ms	14×	body	160	valid
1.0ms	3×	body	320	invalid
1.0ms	5×	body	160	nan
1.0ms	15×	body	80	nan
1.0ms	5×	body	80	invalid
0.0ms	2×	body	160	invalid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5194	19

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 35.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.1b	(pow.f64 x (/.f64 1 n))
2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`pow-unpow_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
17×	`unpow-prod-down_binary64`
9×	`difference-of-squares_binary64`
8×	`sqr-pow_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
6.0ms	(pow.f64 x (/.f64 1 n))
9.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
47.0ms	(pow.f64 x (/.f64 1 n))
129.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify93.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4928	1611
1	4928	1611

prune115.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Merged error: 24.4b

Counts

88 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)
0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.1b	(pow.f64 x (/.f64 1 n))
2.4b	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
47×	`unpow-prod-down_binary64`
33×	`*-un-lft-identity_binary64`
29×	`pow-unpow_binary64`
27×	`difference-of-squares_binary64`
25×	`add-cube-cbrt_binary64`
24×	`cbrt-prod_binary64`
23×	`sqr-pow_binary64`
18×	`times-frac_binary64`
17×	`cube-prod_binary64`
8×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `pow-exp_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow-to-exp_binary64`
3×	`distribute-lft-out_binary64` `pow-pow_binary64`
2×	`div-inv_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 129

Calls

4 calls:

6.0ms	(pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
3.0ms	(pow.f64 x (/.f64 1 n))
17.0ms	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)
53.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
44.0ms	(pow.f64 x (/.f64 1 n))
135.0ms	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))

simplify84.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5006	3081

prune121.0ms

Filtered

85 candidates to 141 candidates (-65.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	141	8	149

Merged error: 24.3b

Counts

149 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.1b	(exp.f64 (/.f64 (log.f64 x) n))
0.3b	(/.f64 (log.f64 x) n)
2.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `times-frac_binary64`
29×	`add-cube-cbrt_binary64`
16×	`exp-prod_binary64`
13×	`pow-unpow_binary64`
12×	`pow1_binary64`
7×	`add-log-exp_binary64` `log-pow_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`unpow-prod-down_binary64`
4×	`associate-/l*_binary64` `div-inv_binary64`
3×	`associate-/r*_binary64` `difference-of-squares_binary64`
2×	`sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64` `exp-to-pow_binary64` `pow-exp_binary64`

Counts

4 → 99

Calls

4 calls:

5.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(exp.f64 (/.f64 (log.f64 x) n))
4.0ms	(/.f64 (log.f64 x) n)
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
43.0ms	(exp.f64 (/.f64 (log.f64 x) n))
34.0ms	(/.f64 (log.f64 x) n)
130.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

simplify135.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4913	1717
1	4913	1717

prune86.0ms

Filtered

78 candidates to 111 candidates (-42.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	110	9	119

Merged error: 24.3b

Counts

119 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.1b	(pow.f64 E.f64 (/.f64 (log.f64 x) n))
0.3b	(/.f64 (log.f64 x) n)
2.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 E.f64 (/.f64 (log.f64 x) n)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
33×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
29×	`pow-unpow_binary64`
13×	`pow1_binary64` `unpow-prod-down_binary64`
9×	`difference-of-squares_binary64`
8×	`sqr-pow_binary64` `add-exp-log_binary64`
7×	`log-pow_binary64`
6×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/r*_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `e-exp-1_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`

Counts

4 → 111

Calls

4 calls:

6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 E.f64 (/.f64 (log.f64 x) n))
6.0ms	(/.f64 (log.f64 x) n)
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 E.f64 (/.f64 (log.f64 x) n)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
60.0ms	(pow.f64 E.f64 (/.f64 (log.f64 x) n))
40.0ms	(/.f64 (log.f64 x) n)
142.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 E.f64 (/.f64 (log.f64 x) n)))

simplify84.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5607	2178

prune92.0ms

Filtered

87 candidates to 123 candidates (-41.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	5	6
Picked	1	0	1
Done	1	1	2
Total	123	9	132

Merged error: 24.3b

Counts

132 → 9

regimes143.0ms

Accuracy

85.1% (1.6b remaining)

Error of 24.0b against oracle of 22.4b and baseline of 33.1b

bsearch2.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	78	116
1	78	116

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.1s	3774×	body	1280	valid
1.1s	1013×	body	1280	nan
727.0ms	1590×	body	640	valid
686.0ms	942×	body	640	nan
478.0ms	2616×	body	80	overflowed
229.0ms	740×	body	320	valid
209.0ms	467×	body	320	nan
181.0ms	259×	body	640	invalid
153.0ms	115×	body	1280	invalid
148.0ms	1578×	body	80	valid
72.0ms	164×	body	320	invalid
66.0ms	318×	body	160	valid
51.0ms	219×	body	160	nan
35.0ms	248×	body	80	invalid
33.0ms	526×	body	80	nan
19.0ms	77×	body	160	invalid

Details

analyze1.1s

sample230.0ms

simplify85.0ms

prune2.0ms

localize9.0ms

rewrite25.0ms

series229.0ms

simplify93.0ms

prune115.0ms

localize11.0ms

rewrite38.0ms

series364.0ms

simplify84.0ms

prune121.0ms

localize11.0ms

rewrite26.0ms

series262.0ms

simplify135.0ms

prune86.0ms

localize13.0ms

rewrite29.0ms

series298.0ms

simplify84.0ms

prune92.0ms

regimes143.0ms

bsearch2.0ms

simplify4.0ms

end0.0ms

sample6.6s

Profiling